Regardless of how your mental mapping of their marketing copy works, they've been completely explicit about the fact that Basecamp is not designed for people who want fine-grained schedule-based management. They've written extremely popular blog posts about why they think that kind of project management is evil. You can agree or disagree with that (I do both), but you can't tell them they have to add features they don't want to add just because you have a different definition of "project management".
But, Basecamp is a project management tool. It allows you to track tasks (and due-dates), and milestones. I don't care about task dependancies, or gannt charts.
I do care about agile development. I do need to see the status of my project in an aggregate way (are we close yet?) Even understanding that estimates are wild guesses, task-level timeboxing is better than working backwards from dates. I can't image the due-date feature working well except for in some very narrow circumstances.
I guess overall if my definition is "project management" is different, then wouldn't they want their product to work to handle users like me? Or not, and that's okay. I'm just saying that I'm cut out of the niche of users they are looking for, whether it be intentional or not.
Like the commenter downthread said, you want Pivotal Tracker, not Basecamp.